Before learning this unit you must be able to add subtract multiply and divide whole numbers. you also must be able to solve a simple equation. Finally you must have a basic understanding of fractions. After this unit you should be able to follow order of operations, Simplify fractions and convert decimals percents and fractions. A very common misconception is when simplifying fractions someone will divide by the wrong number. The key pieces of information are pemdas and how to move the decimal around while converting.
Unit 1
1) Order of operations 1+3x2/2 1+6/2 1+3 4 Pemdas is the simplest way to remember the order of operations. Each letter stands for an operation. P is parenthesis, in this you do everything that is inside any parenthesis. E stands for exponents, you must do all exponents in the problem. M and D stand for multiplication and division, you then do all multiplication and division in the problem from left to right. Then finally there is A and S which stand for addition and subtraction, you add and subtract from left to right. An easy way to remember PEMDAS is a saying. The most common saying goes Please Excuse My Dear Aunt Sally, Each word starts with the next letter in PEMDAS.
Pemdas is used forever Even on the sat’s where it is more advanced with multiple parenthesis.
7x2+(7+3x[ 5-2] ) -4x2 7x2+(7+3x[3] ) -4x2 7x2+(7+9 ) -4x2 7x2+16 -4x2 14+16 -4x2 14+16 -8 30-8 22 Although this problem is much more complex than usual math problems you still follow PEMDAS. When there are parenthesis, you follow the order of operations inside them. You will always use Order of operations.
2) Simplifying, adding, and subtracting, fractions
Fractions are an important part of mathematics. They represent Pieces of a whole. Fractions are easily explain using a pie or a pizza.
Real life example. If a pizza is cut into four equal pieces and one is eaten by paul, There are Three fourths or ¾ of the pizza left. Paul ate One fourth or ¼ pieces because there were 4 pieces and he ate one of them so you put the number of pieces taken over the whole number of pieces. If pauls friend suzy ate another piece of his pizza there would be 2/4 pieces of pizza left. 2/4 can be simplified. If the denominator (number on the bottom) is divisible by the numerator (number on the top) the number is able to be simplified. you simply (pun intended) divide the bottom and top number by the top number to get the simplified version. Take 2/4 as an example if you divide 2 by 2 you get 1, and if you divide 4 by 2 you get 2. So your new fraction would be ½.
You also need to add and subtract fractions. When adding and subtracting fractions ONLY the top number is changed.
1/3 +3/3 = 4/3 3/3 - 1/3 = 2/3 If you get a fraction where there is a bigger number on top this is called a mixed number. Mixed numbers are simplified by dividing the top number by the bottom number, most of the time there will be a remainder. this remainder goes back over the denominator.
4/3 = 1⅓ 6/3 = 2
3) Convert decimals, to percent, and fractions
Converting between these three things is very easy. To convert from a decimal to a percent or a percent to a decimal all you do is move the point two places to the right for a percent or to the left to get back to a decimal. Here is an example.
.23 if you move the decimal two places to the right it becomes a percent 23% If you start with a percent 45%, then you move the point to the left it becomes .45, a decimal
Converting from a fraction to a decimal is also simple, you divide the numerator, or the number on top by the denominator or the number on the bottom.
½ = .5 ¼ = .25
converting from a decimal to a fraction is simple. first put the decimal over one and then multiply the top and bottom by ten for each number after the decimal. finally you just have to simplify.
Before learning this unit you must be able to add subtract multiply and divide whole numbers. you also must be able to solve a simple equation. Finally you must have a basic understanding of fractions. After this unit you should be able to follow order of operations, Simplify fractions
and convert decimals percents and fractions. A very common misconception is when simplifying fractions someone will divide by the wrong number. The key pieces of information are pemdas and how to move the decimal around while converting.
Unit 1
1)
Order of operations 1+3x2/2
1+6/2
1+3
4
Pemdas is the simplest way to remember the order of operations. Each letter stands for an operation. P is parenthesis, in this you do everything that is inside any parenthesis. E stands for exponents, you must do all exponents in the problem. M and D stand for multiplication and division, you then do all multiplication and division in the problem from left to right. Then finally there is A and S which stand for addition and subtraction, you add and subtract from left to right. An easy way to remember PEMDAS is a saying. The most common saying goes Please Excuse My Dear Aunt Sally, Each word starts with the next letter in PEMDAS.
Pemdas is used forever Even on the sat’s where it is more advanced with multiple parenthesis.
7x2+(7+3x[ 5-2] ) -4x2
7x2+(7+3x[3] ) -4x2
7x2+(7+9 ) -4x2
7x2+16 -4x2
14+16 -4x2
14+16 -8
30-8
22
Although this problem is much more complex than usual math problems you still follow PEMDAS. When there are parenthesis, you follow the order of operations inside them. You will always use Order of operations.
2) Simplifying, adding, and subtracting, fractions
Fractions are an important part of mathematics. They represent Pieces of a whole. Fractions are easily explain using a pie or a pizza.
Real life example. If a pizza is cut into four equal pieces and one is eaten by paul, There are Three fourths or ¾ of the pizza left. Paul ate One fourth or ¼ pieces because there were 4 pieces and he ate one of them so you put the number of pieces taken over the whole number of pieces. If pauls friend suzy ate another piece of his pizza there would be 2/4 pieces of pizza left. 2/4 can be simplified. If the denominator (number on the bottom) is divisible by the numerator (number on the top) the number is able to be simplified. you simply (pun intended) divide the bottom and top number by the top number to get the simplified version. Take 2/4 as an example if you divide 2 by 2 you get 1, and if you divide 4 by 2 you get 2. So your new fraction would be ½.
You also need to add and subtract fractions. When adding and subtracting fractions ONLY the top number is changed.
1/3 +3/3 = 4/3 3/3 - 1/3 = 2/3
If you get a fraction where there is a bigger number on top this is called a mixed number. Mixed numbers are simplified by dividing the top number by the bottom number, most of the time there will be a remainder. this remainder goes back over the denominator.
4/3 = 1⅓ 6/3 = 2
3) Convert decimals, to percent, and fractions
Converting between these three things is very easy. To convert from a decimal to a percent or a percent to a decimal all you do is move the point two places to the right for a percent or to the left to get back to a decimal. Here is an example.
.23 if you move the decimal two places to the right it becomes a percent 23%
If you start with a percent 45%, then you move the point to the left it becomes .45, a decimal
Converting from a fraction to a decimal is also simple, you divide the numerator, or the number on top by the denominator or the number on the bottom.
½ = .5 ¼ = .25
converting from a decimal to a fraction is simple. first put the decimal over one and then multiply the top and bottom by ten for each number after the decimal. finally you just have to simplify.